669 Weinberg Can Science Explain Everything Anything.pdf

Volume 48, Number 9 · May 31, 2001

Feature

Can Science Explain Everything? Anything?
By Steven Weinberg One evening a few years ago I was with some other faculty members at the University of Texas, telling a group of undergraduates about work in our respective disciplines. I outlined the great progress we physicists had made in explaining what was known experimentally about elementary particles and fields—how when I was a student I had to learn a large variety of miscellaneous facts about particles, forces, and symmetries; how in the decade from the mid-1960s to the mid-1970s all these odds and ends were explained in what is now called the Standard Model of elementary particles; how we learned that these miscellaneous facts about particles and forces could be deduced mathematically from a few fairly simple principles; and how a great collective Aha! then went out from the community of physicists. After my remarks, a faculty colleague (a scientist, but not a particle physicist) commented, "Well, of course, you know science does not really explain things—it just describes them." I had heard this remark before, but now it took me aback, because I had thought that we had been doing a pretty good job of explaining the observed properties of elementary particles and forces, not just describing them.[1] I think that my colleague's remark may have come from a kind of positivistic angst that was widespread among philosophers of science in the period between the world wars. Ludwig Wittgenstein famously remarked that "at the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena." It might be supposed that something is explained when we find its cause, but an influential 1913 paper by Bertrand Russell had argued that "the word 'cause' is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable."[2] This left philosophers like Wittgenstein with only one candidate for a distinction between explanation and description, one that is teleological, defining an explanation as a statement of the purpose of the thing explained. E.M. Forster's novel Where Angels Fear to Tread gives a good example of teleology making the difference between description and explanation. Philip is trying to find out why his friend Caroline helped to bring about a marriage between Philip's sister and a young Italian man of whom Philip's family disapproves. After Caroline reports all the conversations she had with Philip's sister, Philip says, "What you have given me is a description, not an explanation." Everyone knows what Philip means by this—in asking for an explanation, he wants to learn Caroline's purposes. There is no purpose revealed in the laws of nature, and not knowing any other way of distinguishing description and explanation, Wittgenstein and my friend had concluded that these laws could not be explanations. Perhaps some of those who say that science describes but does not explain mean also to compare science unfavorably with theology, which they imagine to explain things by reference to some sort of divine purpose, a task declined by science.

This mode of reasoning seems to me wrong not only substantively, but also procedurally. It is not the job of philosophers or anyone else to dictate meanings of words different from the meanings in general use. Rather than argue that scientists are incorrect when they say, as they commonly do, that they are explaining things when they do their work, philosophers who care about the meaning of explanation in science should try to understand what it is that scientists are doing when they say they are explaining something. If I had to give an a priori definition of explanation in physics I would say, "Explanation in physics is what physicists have done when they say Aha!" But a priori definitions (including this one) are not much use.

not vice versa. and Robert Hooke all used Kepler's relation between the squares of the periods and the cubes of the diameters (taking the orbits as circles) to deduce an inverse square law of gravitation. and the squares of the periods (the times it takes the various planets to go around their orbits) are proportional to the cubes of the major diameters of the planets' orbits. and it is in that sense that Newton's laws explain Kepler's laws rather than the other way around. while Kepler's laws deal with the more limited context of planetary motions. to paraphrase something that Mary McCarthy once said about a book by Lillian Hellman. of course."[4] But this doesn't remove the difficulty. and Wesley Salmon. It is tempting to say that more fundamental means more comprehensive. So there is a sense in which Kepler's laws have a generality that Newton's laws don't have.As far as I can tell. Carl Hempel. But it's not easy to put a precise meaning to the idea that one physical principle is more fundamental than another. One might say for instance that Newton's laws govern not only the motions of planets but also the tides on Earth. There is a large modern literature on the nature of explanation. which captures what physicists mean when they say that they have explained some regularity. I gather that philosophers are now going about this the right way: they are trying to develop an answer to the question "What is it that scientists do when they explain something?" by looking at what scientists are actually doing when they say they are explaining something. Somewhat earlier. From what I have read in this literature." But here I will focus on the three words that I think present the greatest difficulties: the words "fundamental. Kepler's laws. Unfortunately. The answer is that we explain a physical principle when we show that it can be deduced from a more fundamental physical principle.. Yet it would feel absurd to say that
. the blizzard of 1888. Perhaps the best-known attempt to capture the meaning that scientists give to explanation was that of Carl Hempel. because deduction itself doesn't carry a sense of direction. Everyone knows that Newton discovered not only a law that says the force of gravity decreases with the inverse square of the distance. the French Revolution. Kepler had described three laws of planetary motion: planets move on ellipses with the sun at the focus. the line from the sun to any planet sweeps over equal areas in equal times. In his well-known 1948 article written with Paul Oppenheim. such as the extinction of the dinosaurs. because philosophers of science have had trouble with the question of what is meant by an explanation of an event (note Wittgenstein's reference to "natural phenomena") while physicists are interested in the explanation of regularities. this has become well understood by philosophers of science at least since World War II. and so on. and so on are concerned with the causes of individual events. as well as to philosophers. We have a deep sense that Newton's laws are more fundamental than Kepler's laws. where gravity is irrelevant. under a more general law. but which of the infinite number of things that could affect an event should be regarded as its cause?[3] Within the limited context of physics. when you study mechanics you learn to deduce Kepler's laws from Newton's laws. while a physicist only becomes interested in an event. every word in this definition has a questionable meaning. Today. and then Newton extended the argument to elliptical orbits. Philip Kitcher. Philip Kitcher has tried to revive the idea that the way to explain an event is by reference to its cause. The best example I know is provided by the relation between the laws of Newton and the laws of Kep-ler. meteorologists. I think one can give an answer of sorts to the problem of distinguishing explanation from mere description. by philosophers like Peter Achinstein. the falling of fruits from trees. This task seems to me to be a bit easier in physics (and chemistry) than in other sciences. like the fogging of Becquerel's photographic plates that in 1897 were left in the vicinity of a salt of uranium. Edmund Halley. such as the instability of the uranium atom. he remarked that "the explanation of a general regularity consists in subsuming it under another more comprehensive regularity. historians."
The troublesome word "fundamental" can't be left out of this definition. of physical principles. It is usual to say that Newton's laws explain Kepler's. also govern the motion of electrons around the nucleus. Biologists. but also a law of motion that tells how bodies move under the influence of any sort of force. But that isn't strictly true. when the event reveals a regularity of nature. etc. Scientists who do pure rather than applied research commonly tell the public and funding agencies that their mission is the explanation of something or other." "deduced. to the extent that classical mechanics applies at all." and "principle. it often works both ways. But historically Newton's law of gravitation was deduced from Kepler's laws of planetary motion. rather than of individual events. including "we" and "a. Christopher Wren. so the task of clarify-ing the nature of explanation can be pretty important to them.

as in general relativity. But they don't apply everywhere. the photon. If three people agree that each one will measure the angle between the lines of sight to the other two. This example of Newton's and Kep-ler's laws is a bit artificial. Nevertheless. it has been shown that any particle whose mass is zero and whose spin is equal to two will behave just the way that gravitons do in general relativity. even though it was resisted by Max Planck. Ernst Zermelo. while everyone (except perhaps a philosophical purist) is comfortable with the statement that Newton's laws explain Kepler's. Further. or on some theory like string theory that predicts the existence of gravitons?
The idea of explanation as deduction also runs into trouble when we consider physical principles that seem to transcend the principles from which they have been deduced. It is important here to distinguish two different aspects of thermodynamics. After the laws of thermodynamics had been formulated in the nineteenth century. And you will get the same 180-degree result for the sum of the angles of a triangle made of steel bars or of pencil lines on a piece of paper. This is especially true of thermodynamics. On one hand. In other cases the question of what explains what is more difficult. Here is an example. I don't see much difference between thermodynamics and Euclidean geometry. twice the spin of the photon). As we learned from Einstein's general theory of relativity. and to many other systems. The laws apply to black holes. So thermodynamics seems to transcend the statistical mechanics of many-body systems from which it was originally deduced. When we use Euclidean geometry to explain anything in nature we are tacitly relying on general relativity to explain why Euclidean geometry applies in the case at hand. it is a general prediction of string theory that there must exist particles of mass zero and spin two. the sum will be 180 degrees. In this respect. and that the exchange of these gravitons will produce just the gravitational effects that are predicted by general relativity. sometimes they can't. Ludwig Boltzmann succeeded in deducing these laws from statistical mechanics. Euclidean geometry applies in an astonishing variety of contexts. though it is a very good approximation in the relatively weak gravitational field of the earth in which it was developed by Euclid.
. On the other hand. but have a spin equal to two (that is. After all. But Euclidean geometry is a formal system of inference based on postulates that may or may not apply in a given situation. and a few other physicists who held on to the older view of the laws of thermodynamics as free-standing physical principles. Boltzmann's explanation of thermodynamics in terms of statistical mechanics became widely accepted. as fundamental as any others. wherever those laws apply. because there is no real doubt about which is the explanation of the other. To find out whether the laws of thermodynamics apply to a particular physical system. and not because they are composed of many molecules. like the particle of light.Kepler's laws explain Newton's. or is the general theory of relativity explained by the existence of the graviton? We don't know. On the answer to this question hinges a choice of our vision of the future of physics—will it be based on space-time geometry. they apply to steam boilers. Thermodynamics itself is never the explanation of anything—you always have to ask why thermodynamics applies to whatever system you are studying. thermodynamics is a formal system that allows us to deduce interesting consequences from a few simple laws. Thermodynamics would have no meaning if applied to a single atom. and you do this by deducing the laws of thermodynamics from whatever more fundamental principles happen to be relevant to that system. the science of heat and temperature and entropy. but simply because they have a surface from which no particle or light ray can ever emerge. the Euclidean system does not apply in gravitational fields. So is the existence of the graviton explained by the general theory of relativity. When quantum mechanics is applied to Einstein's general theory of relativity one finds that the energy and momentum in a gravitational field come in bundles known as gravitons. you have to ask whether the laws of thermodynamics can be deduced from what you know about that system. and more important. But then the work of Jacob Bekenstein and Stephen Hawking in the twentieth century showed that thermodynamics also applies to black holes. the physics of macroscopic samples of matter that are composed of large numbers of individual molecules. So it may seem that geometry is more fundamental than optics or mechanics. Sometimes they can. particles that have zero mass. and then they get together and add up those angles. I would argue that there is a sense in which the laws of thermodynamics are not as fundamental as the principles of general relativity or the Standard Model of elementary particles.

In this way you develop a large set of linked differential equations. many physicists immediately concluded that all of chemistry is explained by quantum mechanics and the principle of electrostatic attraction between electrons and atomic nuclei. after the development of quantum mechanics in the mid-1920s. you would find that more helium would be produced. but it would not advance our understanding of the laws of nature. The proton mass is produced by the strong forces that the quarks inside the proton exert on one another. because we already understand the strong nuclear force well enough to know that no new laws of nature will be needed in this calculation. I'm not even sure we have a good algorithm for doing the calculation. Physicists were sure that all these chemical properties were consequences of the laws of quantum mechanics as applied to nuclei and electrons. That may sound really peculiar. but still some fairly impressive organic molecules—by doing complicated computer calculations using quantum mechanics and the principle of electrostatic attraction. each term proportional to the abundances of other nuclear species. we now can in fact deduce the properties of fairly complicated molecules—not molecules as complicated as proteins or DNA.
. Physicists like Paul Dirac proclaimed that now all of chemistry had become understood. These calculations also revealed certain regularities. because it can give us a strategic sense of what problems to work on." as physicists say) of any one nuclear species is equal to a sum of terms. if you put something in the theory to speed up the expansion.In talking about deduction. This is somewhat counterintuitive—you might think speeding up the expansion of the universe would leave less time for the nuclear reactions that produce helium. If you want to work on calculating the proton mass. but consider the following little story. but still we know that physics explains why chemicals are the way they are. we run into another problem: Who is it that is doing the deducing? We often say that something is explained by something else without our actually being able to deduce it. not in the sense that we have calculated it or even can calculate it. Chemists do not call themselves physicists. with other elements present only in tiny quantities. For instance. as for instance by adding additional species of neutrinos. more power to you. When physicists started to take the big bang cosmology seriously one of the things they did was to calculate the production of light elements in the first few minutes of the expanding universe. but there is no sense of mystery about the mass of the proton. it's not in our scientific articles. It can be very important to recognize that something has been explained. For example. and Fred Hoyle. When these equations were solved in the mid-1960s by James Peebles and then by Robert Wagoner. and so chemistry persists as a separate discipline. when it became possible to calculate for the first time in a clear and understandable way the spectrum of the hydrogen atom and the binding energy of hydrogen. but in the sense that quantum chromodynamics can calculate it—the value of the proton mass is entailed by quantum chromodynamics. We feel we know why it is what it is. Similar remarks apply to other areas of physical science. but in fact the calculations showed that it increased the amount of helium produced. William Fowler. The way this was done was to write down all the equations that govern the rates at which various nuclear reactions took place. It would be a lovely show of calculational ability. it was found that after the first few minutes one quarter of the mass of the universe was left in the form of helium. and almost all the rest was hydrogen. Experience has borne this out. It's difficult to deal with complicated molecules by the methods of quantum mechanics. The rate of change of the quantity (or "abundance. It is not that we can actually calculate the proton mass. even in this limited sense. go ahead. it's in nature. and then you put them on a computer that produces a numerical solution. As part of the Standard Model. we have a wellverified theory of the strong nuclear force—the force that binds together both the particles in the nucleus and the particles that make up those particles—known as quantum chromodynamics. The explanation is not in our books. But they had not yet succeeded in deducing the chemical properties of any molecules except the simplest hydrogen molecule.
Another problem with explanation as deduction: in some cases we can deduce something without explaining it. even though we don't know how to do the calculation. they have different journals and different skills from physicists. it is that the laws of physics require chemicals to behave the way they do. But chemical phenomena will never be entirely explained in this way. Almost any physicist would say that chemistry is explained by quantum mechanics and the simple properties of electrons and atomic nuclei. which we believe explains why the proton mass is what it is.

Sometimes what we think is a fundamental law of nature is just an accident. the earlier the temperature dropped to a billion degrees.
. just as free neutrons do in our laboratories today. one answer would be that if the earth were much closer to the sun then it would be too hot for us and if it were any further from the sun then it would be too cold for us. the question why the laws of nature that we discover and the constants of nature that we measure are what they are would have a rough teleological explanation—that it is only with this sort of big bang that there would be anyone to ask the question. it should be no surprise that creatures that inquire into the distance of their planet from its star would find that they live on one of the planets in this tiny fraction. a particularly stable nucleus. Therefore the crucial thing that determines the amount of helium produced in the early universe is how many of the neutrons decayed before the temperature dropped to a billion degrees. so that even if only a tiny fraction are the right distance from their star and have the right mass and chemical composition and so on to allow life to evolve. But there is a sense in which that explanation is not so silly. In a sense. That's the explanation of what was found in the computer calculations. During all this time neutrons were changing into protons. although I have said that physicists are only interested in explaining general principles. Cosmologists increasingly speculate that just as the earth is just one of many planets. and perhaps even some of what we now call the laws of nature take different forms. But we have to keep in mind the possibility that what we now call the laws of nature and the constants of nature are accidental features of the big bang in which we happen to find ourselves. as opposed. to two hundred million or fifty million miles. at the end of the first three minutes. Further. or even closer. and so the more helium was produced. so the less time the neutrons had to decay. While the universe was expanding and cooling in the first few minutes. and then by combining deuterons with protons or neutrons or other deuterons to make heavier nuclei like helium. Today we smile at this because we know that the distances of the planets from the sun reflect accidents that occurred as the solar system happened to be formed. because we know that there was no advance knowledge of human beings in the formation of the solar system. and as you can see it does not offer a terribly useful insight into the physics of the solar system. nuclear reactions were occurring that built up complex nuclei from the primordial protons and neutrons. We wouldn't try to explain the diameters of the planetary orbits by deducing them from some fundamental law. though it can't easily be seen in the computer printout. say. But anthropic arguments may become very important when applied to what we usually call the universe. They further speculate that in these many different big bangs some of the supposed constants of nature take different values. He is known today chiefly for his famous three laws of planetary motion. so essentially no deuterons were produced until the temperature had dropped to about a billion degrees. When the temperature dropped to a billion degrees. however. that's a pretty silly explanation. may be just one of many bangs that go off sporadically here and there in a much larger mega-universe. so the more of them were left. the great expansion of the universe in which we live. This kind of explanation is known as anthropic. and the deuterons then into helium. but the explanation was not to be found in the computer-generated graphs showing the abundance in relation to the speed of expansion. there is a kind of approximate statistical explanation for the distance of the earth from the sun. though constrained (as is the distance of the earth from the sun) by the requirement that they have to be in a range that allows the appearance of beings that can ask why they are what they are. Kepler again provides an example. but because the density of matter was relatively low these reactions could occur only sequentially. then all of the neutrons that were still left were rapidly gobbled up into deuterons. so also our big bang. In this case. and it became cold enough for deuterons to hold together. The faster the expansion went. I certainly hope that we will not be driven to this sort of reasoning. the deuteron. first by combining some protons and neutrons to make the nucleus of heavy hydrogen. because there are countless planets in the universe.[5] If you ask why the earth is about a hundred million miles from the sun. they're relatively weakly bound. or even further. and that we will discover a unique set of laws of nature that explain why all the constants of nature are what they are. but when he was a young man he tried also to explain the diameters of the orbits of the planets by a complicated geometric construction involving regular polyhedra. it is not so clear what is a principle and what is a mere accident. However. deuterons are very fragile.The explanation is not difficult. As it stands. It takes two neutrons as well as two protons to make a helium nucleus. so the number of helium nuclei produced at that time was just half the number of remaining neutrons.

why John Wilkes Booth's bullet killed Lincoln while the Puerto Rican nationalists who tried to shoot Truman did not succeed.
I have now done the best I can to say whether science can explain anything. that in physics we say that we explain a principle when we deduce it from a more fundamental principle? Yes. So now that I have deconstructed the words "fundamental. science can never explain any moral principle. I suspect that this was because Aristotle implicitly assumed that the rates at which the elements move to their natural places are mere accidents. We cannot explain. from which all other regularities can be deduced. what facts about nature are entailed by what principles. There certainly always will be accidents that no one will explain. that you couldn't say anything general about them (except that heavy objects fall faster than light ones). we don't. you might consider a theory that Southern actors in the mid-nineteenth century tended to be good shots while Puerto Rican nationalists in the mid-twentieth century tended to be bad shots." is anything left of my proposal. for example. the natural position of fire is upward. Of course Aristotle was wrong about this. laws of nature." "deduce. a prediction of the sort that Newton's laws do provide? According to Aristotle. based on a few simple principles. He did not seem to realize that this was a problem that anyone ought to solve. Why was Aristotle (and many other natural philosophers. for instance. events depend on accidents that we can never recover. There seems to be an unbridgeable gulf between "is"
. We have been steadily moving toward a satisfying picture of the world. These laws will be the explanation of whatever principles (such as. but Aristotle did not try to say how fast a bit of earth drops downward or a spark flies upward. What puzzles me is why Aristotle expressed no dissatisfaction that he had not learned how to calculate the positions of projectiles at each moment along their paths. I think there is. but only within a historical context. and water and air are naturally somewhere in between. but if you imagine yourself in his times. which was admired by Aristotle's teacher Plato. that the only things about which one could generalize were questions of equilibrium— where objects will come to rest. but when you only have a few singular pieces of information it's very difficult to make even statistical inferences. Physicists try to explain just those things that are not dependent on accidents. We might have a partial explanation if we had evidence that one of the gunmen's arms was jostled just as he pulled the trigger. and so on. Further. that they are not subject to rules. This may have reflected a widespread disdain for change on the part of the Hellenic philosophers. Only when we have this final theory will we know for sure what is a principle and what an accident. All such information is lost in the mists of time. but because we never will know all these conditions. but in the real world most of what we try to understand does depend on accidents. as shown for instance in the work of Parmenides. it is also possible that a class of phenomena may be regarded as mere accidents when in fact they are manifestations of fundamental physical principles. the rules of the Standard Model or of general relativity) can be deduced directly from them. this was not understood until Galileo began to measure how long it took balls to roll various distances down an inclined plane. We can perhaps try to explain them statistically: for example. I am not asking why Aristotle had not discovered Newton's laws—obviously someone had to be the first to discover these laws. and about this we cannot always know in advance. substances tend to move to their natural positions—the natural position of earth is downward. and which are the fundamental principles and which are the less fundamental principles that they explain. a vision of the future of science. Clearly not. It is one of the great tasks of science to learn what are accidents and what are principles. and the prize happened to go to Newton. notably Descartes) satisfied with a theory of motion that did not provide any way of predicting where a projectile or other falling body would be at any moment during its flight. We hope that in the future we will have achieved an understanding of all the regularities that we see in nature. as it happens. As far as I know. and those directly deduced principles will be the explanations of whatever principles can be deduced from them. you can see how far from obvious it would have been that motion is governed by precise mathematical rules that might be discovered.Conversely. so let me take up the question whether science can explain everything. There are questions like why the genetic code is precisely what it is or why a comet happened to hit the earth 65 million years ago in just the place it did rather than somewhere else that will probably remain forever outside our grasp." and "principle. not because they could not be explained if we knew all the precise conditions that led up to them. I think this may be the answer to a historical question that has puzzled me for many years. but.

that our species has evolved in such a way that men and women play different roles—men hunt and fight. but they are all impoverished. there are no people. and if it does then I think that physicists will be at the extreme limits of their power of explanation. and it certainly is the one that would be most relevant politically. we still wouldn't be certain that they are true. If you could trace the sequence of events that led from the syphilis to the paresis. We can perhaps explain why people think they should do things. The only kind of explanation I can imagine (if we are not just going to find a deeper set of laws.questions and "ought" questions. pp. Perhaps this is because the syphilis is the most dramatic of the many causes that led to the effect. like Newton's laws describing a few particles endlessly orbiting each other in accordance with these laws.) I think that in the end we will come to a set of simple universal laws of nature. Vol. but it remains open to us to transcend these biologically based moral rules. the quarks and the gluons. if you take the Standard Model of elementary particles and just throw away everything except the strong nuclear forces and the particles on which they act.J. 135 (1948). If you give up quantum mechanics and relativity then you can make up a huge variety of other logically consistent laws of nature. reprinted with some changes in Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (Free Press.
[5]
Professor R. The moral postulates that tell us whether we should or should not do so cannot be deduced from our scientific knowledge. Is this explained by the fact that the mayor had an untreated case of syphilis some years earlier? The trouble with this explanation is that most people with untreated syphilis do not in fact get paresis. 1957). You give up worrying about certainty when you make that turn in your career that makes you a physicist rather than a mathematician. For example. Perhaps our best hope for a final explanation is to discover a set of final laws of nature and show that this is the only logically consistent rich theory. that doesn't worry me. it seems clear that we will never be able to explain our most fundamental scientific principles. Hankinson of the University of Texas has directed my attention to Galen for an early
. It seems that quantum chromodynamics is mathematically selfconsistent. Well. but it describes an impoverished universe in which there are only nuclear particles—there are no atoms. I don't think we'll ever be certain about any of them. No. 174." reprinted in Mysticism and Logic (Doubleday. are completely consistent mathematically but that do not describe nature as we observe it.
[4]
Carl Hempel and Paul Oppenheim.
There is an example of the difficulty of explaining events in terms of causes that is much cited by philosophers.
[2] [3]
[1]
"On the Notion of Cause. p." Philosophy of Science. it seems likely that we will never be able to prove that the most fundamental laws of nature are mathematically consistent. (Maybe this is why some people say that science does not provide explanations. because even if we knew that the laws of nature are mathematically consistent. for example. 135–175. or why the human race has evolved to feel that certain things should be done and other things should not. 1965). with nothing else in the universe. Finally. rich enough for example to allow for the existence of ourselves. "Studies in the Logic of Confirmation. 15. while women give birth and care for children—but we can try to work toward a society in which every sort of work is as open to women as it is to men. you are left with the theory known as quantum chromodynamics. But this is clearly impossible. Just as there are deep mathematical theorems that show the impossibility of proving that arithmetic is consistent. which would then just push the question farther back) would be to show that mathematical consistency requires these laws. There are also limitations on the certainty of our explanations. and nothing new ever happening. These are logically consistent theories. It may be. perhaps the mayor also had some vitamin deficiency — who knows? And yet we feel that in a sense the mayor's syphilis is the explanation of his paresis. as far as we can tell. Suppose it is discovered that the mayor has paresis. but by this reasoning nothing else does either. laws that we cannot explain. This may happen in a century or two. you would discover a great many other things that played an essential role— perhaps a spirochete wiggled one way rather than another way. because we can already imagine sets of laws of nature that.
Notes
This article is based on a talk given at a symposium on "Science and the Limits of Explanation" at Amherst last autumn.